The invention is directed to a system for supplying fluid pressure to a vehicle brake system. Such vehicle brake systems are known. The pressure reservoir of such a vehicle brake system is generally embodied large enough that it can furnish a sufficient amount of pressure medium at sufficiently high pressure to enable full braking with cold brakes, even if the pressure within the pressure reservoir has dropped to near the pressure threshold at which the pump is operating. Initiating a full braking may accordingly trigger the switching on of the pump, which fills the reservoir, causing the pressure at the inlet of the brake valve to rise. Since in full braking initiated at very high speed a considerable loss in friction may occur due to heating of the brake linings, the brake pressure must be increased accordingly. To this end, after the pump has been switched on, a rapid rise in the pressure is required at the inlet of the brake valve, up to a pressure which may be considerably above the pressure threshold for switching on the pump. The pump must have a capacity such that it can fill the pressure reservoir rapidly enough up to this higher pressure. Especially when the pressure reservoir selected is so large that several partial brakings are possible without the aid of a pump, a high-capacity, expensive pump is needed in prior art systems and such a pump has the disadvantage of requiring a powerful supply of electric current for its electric motor. If the vehicle brake system is equipped with anti-skid control valves for repeatedly reducing the brake pressure, then the pump must furthermore also be capable of re-supplying the brake valve with the quantities of pressure medium bled from the brake cylinders during the brake pressure reduction. This further increases the weight and the price of the pump.